1. Field of the Invention
This invention relates to bandgap voltage reference circuits, and more particularly to such circuits in which an attempt is made to correct for a Tln(T) deviation from linearity in the output voltage.
2. Description of the Prior Art
Bandgap reference circuits have been developed to provide a stable voltage supply that is insensitive to temperature variations over a wide temperature range. These circuits operate on the principle of compensating the negative temperature drift of a bipolar transistor's base-emitter voltage (V.sub.be) with the positive temperature coefficient of the thermal voltage V.sub.T, which is equal to kT/q, where k is Boltzmann's constant, T is the absolute temperature in degrees Kelvin and q is the electronic charge. A known negative temperature drift due to V.sub.be is first generated. A positive temperature drift due to the thermal voltage is then produced, and is scaled and subtracted from the negative temperature drift to obtain a nominally zero temperature dependence. Numerous variations in the bandgap reference circuitry have been designed, and are discussed for example in Grebene, Bipolar and MOS Analog Integrated Circuit Design, John Wiley & Sons, 1984, pages 206-209.
Although the output of a bandgap voltage cell is ideally independent of temperature, or at least varies linearally with temperature, the outputs of prior cells have been found to include a term that varies with Tln(T), where 1n is the natural logarithm function. Such an output deviation is shown in FIG. 1, in which the bandgap voltage output (V.sub.bg) increases from a value of about 1.2408 volts at -50.degree. C. to about 1.2444 volts at about 45.degree. C., and then returns back to about 1.2408 volts at 150.degree. C. This output deviation is not symmetrical; its peak is skewed about 5.degree. C. below the midpoint of the temperature range.
It is difficult to precisely compensate for the Tln(T) deviation electronically, so simpler approximations have been used. One such circuit is shown in FIG. 2, and is described in U.S. Pat. No. 4,808,908 to Lewis et al., assigned to Analog Devices, Inc., the assignee of the present invention. The circuit includes bipolar npn transistors Q1 and Q2, with the emitter area of Q2 scaled larger than that of Q1 by a factor A. The emitters of Q1 and Q2 are connected together through a resistor R1 that has a relatively low temperature coefficient of resistance (TCR). A second relatively low TCR resistor R2 is connected in series with a relatively high TCR resistor R3 between the R1/Q1 emitter junction and a negative (or ground) voltage bus V-. Q1 and Q2 are provided with collector currents with a constant ratio between the current magnitudes, such as by connecting their collectors respectively to the inverting and non-inverting inputs of an operational amplifier. R1 and R2 are preferably implemented as thin film resistors, with TCRs on the order of 30 ppm (parts per million)/.degree.C.; such low TCRs may be considered to be negligibly small for purposes of the invention. R3 is preferably a diffused resistor having a TCR of typically 1,500-2,000 ppm/.degree.C.
The output voltage V.sub.bg is equal to the sum of V.sub.be for Q1 and the voltage drops across R2 and R3. In the absence of R3, the voltage across R2 can be determined by considering the voltage across R1. This is equal to the difference in V.sub.be for Q1 and Q2; since the emitter of Q2 is larger than the emitter of Q1 but both transistors may carry equal currents, the emitter current density of Q2 will be less than for Q1 and Q2 will accordingly exhibit a smaller V.sub.be. The V.sub.be differential between Q1 and Q2 will have the form V.sub.T ln (Id1/Id2)=V.sub.T ln(A), where I1 and I2 are the absolute emitter currents, and Id1 and Id2 are the emitter current densities of Q1 and Q2, respectively. Since I1 is preferably equal to I2, the current through R2 will be twice the current through R1, so that the voltage across R2 will have the form (2R1/R2)V.sub.T ln(A). Still ignoring R3, the described circuit will exhibit the Tln(T) output deviation mentioned above.
The addition of high TCR resistor R3 approximates a Tln(T) output voltage compensation by producing a square law (T.sup.2) term that is added to V.sub.bg. Since the tail current through R2 is proportional to temperature anyway, adding a significant temperature coefficient by means of the high TCR tail resistor R3 yields a voltage across this resistance that is proportional to T.sup.2. Combining this square law voltage with the voltage across R2 and V.sub.be for Q1 approximately cancels the effect of the Tln(T) deviation.
R3 is preferably a diffused resistor, which is not subject to trimming. However, the resistance values of thin film resistors R1 and R2 can be conveniently adjusted by laser trimming to minimize the first and second derivatives of the bandgap cell output as a function of temperature.
Unfortunately, the square law voltage compensation produced by the FIG. 2 circuit is perfectly symmetrical, as opposed to the skewed parabolic shape of the Tln(T) deviation that actually characterizes the bandgap cell. Thus, the voltage correction that can be achieved with the FIG. 2 circuit is limited. FIG. 3 compares the Tln(T) and T.sup.2 functions, scaled to a normalized value of the correction voltage V.sub.corr. The resulting variation in the net V.sub.bg, plotted on a normalized scale in which zero is the nominal V.sub.bg, is illustrated in FIG. 4. This is a sideways S-shaped curve that exhibits a significant residual temperature coefficient in both the upper and lower portions of the temperature range.